Problem: Solve for $x$ and $y$ using substitution. ${-6x-4y = 10}$ ${x = -2y+9}$
Solution: Since $x$ has already been solved for, substitute $-2y+9$ for $x$ in the first equation. ${-6}{(-2y+9)}{- 4y = 10}$ Simplify and solve for $y$ $12y-54 - 4y = 10$ $8y-54 = 10$ $8y-54{+54} = 10{+54}$ $8y = 64$ $\dfrac{8y}{{8}} = \dfrac{64}{{8}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {x = -2y+9}\thinspace$ to find $x$ ${x = -2}{(8)}{ + 9}$ $x = -16 + 9$ ${x = -7}$ You can also plug ${y = 8}$ into $\thinspace {-6x-4y = 10}\thinspace$ and get the same answer for $x$ : ${-6x - 4}{(8)}{= 10}$ ${x = -7}$